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11 - Quasi-separable Moore−Penrose Inversion

from Part I - Lectures on Basics with Examples

Published online by Cambridge University Press:  24 October 2024

Patrick Dewilde
Affiliation:
Technische Universität München
Klaus Diepold
Affiliation:
Technische Universität München
Alle-Jan Van der Veen
Affiliation:
Technische Universiteit Delft, The Netherlands
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Summary

This chapter considers the Moore–Penrose inversion of full matrices with quasi-separable specifications, that is, matrices that decompose into the sum of a block-lower triangular and a block-upper triangular matrix, whereby each has a state-space realization given. We show that the Moore–Penrose inverse of such a system has, again, a quasi-separable specification of the same order of complexity as the original and show how this representation can be recursively computed with three intertwined recursions. The procedure is illustrated on a 4 ? 4 (block) example.

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Time-Variant and Quasi-separable Systems
Matrix Theory, Recursions and Computations
, pp. 169 - 182
Publisher: Cambridge University Press
Print publication year: 2024

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